. In an equilateral triangle prove that three times the square


square of one side is equal to four times the square of one of its altitudes.

equilateral triangle

 

Best Answer

Explanation:

We know that if each side of an equilateral triangle is a then the altitude is given by =√3/2a

Three times of square of an side is =3×(a)2=3a2

Four times of square of  an altitude =4×(√3/2×a)2

=4×(√3/2)2×a2

=4×3/4×a2

=3a2

Thus, both are =3a2 , therefore both are equal to each other. 

Three times of square of a side=Four times of square of altitude, proved

Final Answer:

Hence it is proved that three times the square of one side of an equilateral triangle is equal to four times the square of one of its altitudes. 

 

 

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